Trigonometry: What are Gradients?

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SUMMARY

The discussion clarifies the concept of gradians, a unit of angle measurement where a full circle is divided into 400 gradians. It establishes that 180 degrees equals 200 gradians and π radians, with 90 degrees corresponding to 100 gradians. Gradians are particularly utilized in fields such as highway engineering for measuring slopes. The abbreviation "grad" is noted to be ambiguous, as it refers to both "gradian" and "gradient".

PREREQUISITES
  • Understanding of basic trigonometric concepts
  • Familiarity with angle measurement units (degrees, radians, gradians)
  • Knowledge of applications in engineering, particularly in civil engineering
  • Basic proficiency with calculators that include trigonometric functions
NEXT STEPS
  • Research the applications of gradians in civil engineering
  • Learn about the differences between degrees, radians, and gradians
  • Explore the use of trigonometric functions in slope calculations
  • Study the history and development of angle measurement systems
USEFUL FOR

Students, engineers, and professionals in fields requiring precise angle measurements, particularly in civil engineering and architecture.

TSN79
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Just a simple wondering here, the calculator that comes with Windows XP (and other versions) have three choices for trigonometry, degrees, radians, and gradients. I have never heard of this last one, what is it?
 
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It's a gradian-- a unit of angle such that the angle of a full circle is 400 gradians.
 
180 \mbox{degrees} = 200 \mbox{gradients} = \pi \mbox{radians} = \mbox{Angle of a Straight Line}
 
I think the real point is that 90 degrees= \pi/2 radians= 100 gradians. "1 grad" is 1 % of "straight up" and grads are typically used by highway engineers to measure slopes.

It is unfortunate that both "gradian" and "gradient" are abbreviated "grad"!
 

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